Spatial colocation patterns are subsets of spatial feature sets that are frequently “neighboring” in space. In the majority of existing mining methods, neighboring is determined by a single distance threshold and does not take the neighboring degree into consideration causing many neighbor relationships to be lost and they also cannot objectively describe the correlation between spatial features. In addition, existing methods ignore the instance-sharing problem of spatial neighbor relationships when calculating the prevalence of colocation patterns. In order to overcome these weaknesses, this article introduces the fuzzy theory into the spatial colocation pattern discovery. Through the fuzziness of spatial neighbor relationships between spatial instances, we develop a reasonable fuzzy proximity metric, which takes the instance-sharing problem into account and which measures the similarity between different spatial features. Three effective fuzzy clustering methods are proposed, which ensure that colocation patterns can be extracted accurately and quickly. Finally, extensive experiments on five synthetic datasets and five real-world datasets prove the practicability and efficiency of the proposed methods.

The interactions between structured entities play important roles in a wide range of applications such as chemistry, material science, biology, and medical science. Recently, graph-based methods have been exploited to effectively predict the interactions among structured entities. However, these methods usually only focus on structural information of the entities and are incapable of fully utilizing the interaction information between the entities. In this paper, we propose a Denoising Variational Graph of Graphs Auto-encoder (DVGGA) which follows the graph of graphs framework to capture both structural information in structured entities and interaction information among structured entities. With denoising criterion, DVGGA is able to capture the information from the useful structures of the local graph and address the overfitting issue caused by redundant substructures. Extensive experiments conducted on real-world datasets show that DVGGA outperforms the state-of-the-art structured entity interaction prediction methods.